1. Bell work Find the value to make the sentence true. NO CALCULATOR!!
23 = x
5x = 25
(½)3=x
X (1/2) = 5

2. Graph f(x) = 2x
Name 3 points on f(x)
Graph y = x
Graph f-1 (x)
Write an equation for the inverse.

3. F(x) = 2x to write the equation of the inverse, switch the x and y values
x = 2y How do you solve for y? Verbally we would say that “Y is the exponent that 2 to raised to in order to get x.”
To write it mathematically: y = log2x

4. A logarithm is just an exponent
So the inverse of an exponential function is a logarithmic function. (This means that exponentiation “undoes” logarizing and vice versa.)
Definition of logarithm:
X = ay can be rewritten as logax = y
(a>0, a≠1, x>0)
** Why is domain positive? ** What # can be raised to power and give you a negative? **

5. Any exponential expression can be written as a logarithmic expression and vice versa
Rewrite in exponential form.
log28 = 3
log381=4
log164 = ½
log273 = ⅓

6. Any exponential expression can be written as a logarithmic expression and vice versa
Rewrite as a logarithmic expression.
52 = 25
34 = 81
(½)3 = ⅛
(2)-2 = ¼

7. Remember: A logarithm is an exponent
Evaluate.
log216=
** Think: 2 to what power gives me 16?**
log327= _____
log22=_____
log101000=____
2 log31= _____

8. Common logarithm The common logarithm is a log with base of 10.
When the base is 10, we don’t write it!!
Example: log 100 = 2 (Understood base 10)
The calculator uses the common base of 10 when you plug in a value.
Use the calculator to find log 10

9. Natural logarithm The natural logarithm is a log with base e.
Abbreviation is ln
loge5 will be written as ln 5
* “ln” means the base is understood to be e*
What is the value of ln e?

10. Some other important properties that always hold true:
loga1=0
logaa=1
logaax=x
ln1 = 0
ln e = 1
lnex=x

11. Simplify.
log55x
7log714
log51

12. If logax=logay, then x=y
Solve for x:
log2x=log23
Solve for x:
log44= x

13. Steps to graphing a logarithmic function
Rewrite as an exponential equation
Pick values for Y and solve for x
Plot the points.

14. Graph y = log 2x Rewrite as Exponential equation: ___________ Domain:
Range:
Intercepts:
Asymptotes:
How is this related to the graph y =2x?

15. Graph f(x) = log3x
Rewrite as an exponential equation: ___________________
Domain:
Range:
Intercepts:
Asymptotes:

16. Graph y = log 4 x
Rewrite as an exponential equation: ___________________
Domain
Range
Intercepts
Asymtpotes

17. Graph y = lnx Rewrite as an exponential equation: ___________________
Domain:
Range:
Intercepts:
Asymptotes:

18. Graph y = log3(x-2)
Rewrite as an exponential equation: ___________________
Domain:
Range:
Intercepts:
Asymptotes:

19. Transformations What happens to the graph of f(x±c)?
Moves right or left c units
What happens to the graph of f(x) ± c?
Moves the graph up or down c units
What happens to the graph of f(-x)?
Reflects across the y axis
What happens to the graph of –f(x)?
Reflects across the x axis

20. Suppose f(x) = log2x Describe the change in the graph
G(x) = log2(-x)
Reflect over the y axis
G(x) = log2 (x+5)
Moves 5 units to the left, VA: x = -5
G(x) = -log2(x)
Reflect over the x axis
G(x) = log2x-4
Moves the graph down 4 units
g(x) = log 2 (x-3)
Moves the graph 3 units to the right, VA: x = 3

21. Sketch the following graphs Don’t forget RXSRY
Y = -lnx
2. Y = ln(-x)
Y = ln(x-2)
Y = lnx + 3